1.2 The Five-Competency Blueprint & How to Study It
Key Takeaways
- The current test 025 blueprint has five competencies weighted 15% number sense, 30% algebra, 20% geometry, 15% data and probability, and 20% student reasoning and instructional practice.
- The five competencies contain 47 numbered skills in total: 9, 10, 11, 9, and 8 respectively.
- Algebra at 30% is by far the heaviest competency, carrying roughly 15 of about 50 items on its own.
- Florida retired the earlier ten-competency outline for testing after December 31, 2023; guides organized around problem solving, manipulatives, assessment, and connections as separate competencies are out of date.
- Measurement is no longer a standalone competency: unit conversion now sits inside Competency 1 skill 6, and perimeter, area, surface area, and volume sit inside Competency 3 skill 4.
1.2 The Five-Competency Blueprint & How to Study It
Florida publishes a Competencies and Skills document for every FTCE test. For Middle Grades Mathematics 5–9 it lists five competencies, each with an approximate percentage of the total test, and under each competency a numbered list of specific skills. Those numbered skills are the real specification: an item writer must trace every question back to one of them.
The five competencies and their weights
| # | Competency | Weight | Skills | Approx. items of ~50 |
|---|---|---|---|---|
| 1 | Knowledge of number sense, operations, and proportionality | 15% | 9 | ~8 |
| 2 | Knowledge of algebra | 30% | 10 | ~15 |
| 3 | Knowledge of geometry | 20% | 11 | ~10 |
| 4 | Knowledge of data analysis, statistics, and probability | 15% | 9 | ~8 |
| 5 | Knowledge of student reasoning and instructional practice | 20% | 8 | ~10 |
Two observations drive everything else. First, algebra alone is 30% — double the weight of number sense and equal to geometry plus half of data. Second, the four mathematics-content competencies together are 80%, so this is overwhelmingly a content examination with one substantial pedagogy strand rather than a teaching-methods test with some mathematics attached.
The blueprint change you must not miss
Florida redeveloped test 025. The earlier outline had ten competencies — problem solving and reasoning, manipulatives and instructional technology, assessment, connections among concepts, number sense, foundations of algebra, algebraic thinking, data, two-dimensional geometry, and measurement and spatial sense — and it is explicitly marked "For Testing until 12/31/2023." It is retired.
[!WARNING] A great deal of commercial FTCE 025 material still teaches the retired ten-competency outline. You can spot it instantly: if a guide lists "Knowledge of measurement and spatial sense" or "Knowledge of mathematical manipulatives and models and instructional technology" as separate competencies, or quotes weights of 13%, 14%, or 6%, it is built on the outline retired at the end of 2023.
What structurally changed:
- Pedagogy consolidated and shrank. Four separate teaching competencies (problem solving, manipulatives/technology, assessment, connections) totalling 35% became a single 20% competency, Student reasoning and instructional practice.
- Measurement disappeared as a competency. Unit conversion moved into Competency 1 skill 6 alongside ratios and proportions. Perimeter, circumference, area, surface area, and volume moved into Competency 3 skill 4.
- Algebra grew sharply. The old foundations of algebra (14%) plus algebraic thinking (11%) totalled 25%; the single algebra competency is now 30%, and its skill list explicitly adds quadratic key features, quadratic solution methods, exponential growth and decay models, and transformations of function formulas.
- Data and probability nearly doubled, from 7% to 15%, gaining population estimation from surveys and fitting linear functions to bivariate data.
- Trigonometric ratios were dropped. The retired outline tested right-triangle trigonometry; the current geometry competency does not list it. Circles, by contrast, were sharpened into a specific skill about center, radius, and the equation of a circle.
Turning weights into a study plan
Allocate study hours in proportion to weight, then adjust upward for personal weakness. Over a 60-hour plan:
- Algebra — 18 hours. Linear work, quadratics in all three solution methods, exponential models, function families, transformations, and systems.
- Geometry — 12 hours. Formula memorization first, then angle reasoning, congruence and similarity criteria, coordinate geometry, and circles.
- Student reasoning and instructional practice — 12 hours. These items are scenario-based and read quickly, but they hinge on vocabulary you must actually know: learning progressions, the concrete–representational–abstract sequence, formative versus summative use of data, and misconception diagnosis.
- Number sense — 9 hours. Rational number conversion, order of operations, factors, radicals and rational exponents, scientific notation, and proportional reasoning.
- Data and probability — 9 hours. Center and spread, displays, distribution shape, sampling and population estimates, correlation, and theoretical versus experimental probability.
How the competencies interact on real items
Competency 5 items are not free-standing pedagogy. Most of them embed a mathematics task and then ask a teaching question about it — which representation to select, what a student's error reveals, what the next instructional move should be. That means weak content knowledge depresses your Competency 5 score too. A candidate who cannot see why a student wrote (a + b)² = a² + b² cannot choose the right remediation.
The reverse also holds. Content items are frequently dressed in classroom language: a stem may describe a teacher planning a lesson on scale factor and then ask a pure Competency 3 similarity question. Do not let the classroom framing distract you from the mathematics being requested.
A checklist for judging any prep resource
- Does it name five competencies, not ten?
- Does it weight algebra at 30%?
- Does it teach the equation of a circle, completing the square, exponential decay, population estimation from a survey, and learning progressions? All five are current skills that the retired outline did not name.
- Does it avoid promising a specific raw percentage for passing?
If a resource fails these checks, it is teaching a test Florida stopped giving after 2023.
A candidate budgeting 60 study hours by blueprint weight is deciding how much time to give algebra. Using the official approximate percentages, roughly how many hours should algebra receive, and why?
A commercial study guide for test 025 devotes an entire unit to 'Knowledge of measurement and spatial sense (9%)' and another to 'Knowledge of mathematical manipulatives and models and instructional technology (6%).' What does this tell a candidate?
On the current blueprint, where does a question about converting cubic feet to cubic yards belong?